Dr. Malte Gerhold

Postdoctoral researcher at UdS, Saarbrücken

Most recent publications

Baraquin, I.; Franz, U.; Gerhold, M.; Kula, A.; Tobolski, M.: Free resolutions for free unitary quantum groups and universal cosovereign Hopf algebras. Journal of the London Mathematical Society 109(4), e12898, doi:10.1112/jlms.12898.
Gerhold, M.; Varšo, P.: Towards a classification of multi-faced independences: a combinatorial approach. Preprint, arXiv:2301.01816. To appear in Algebraic Combinatorics.
Gerhold, M.; Shalit, O.: Bounded perturbations of the Heisenberg commutation relation via dilation theory. Proceedings of the AMS 151(9), 3949–3957, doi:10.1090/proc/16456.
Diehl, J.; Gerhold, M.; Gilliers, N.: Shuffle Algebras and Non-Commutative Probability for Pairs of Faces. SIGMA Symmetry Integrability Geom. Methods Appl. 19 (2023), Paper No. 006, 50 pp., doi:10.3842/SIGMA.2023.006.
Gerhold, M.; Hasebe, T.; Ulrich, M.: Towards a Classification of Multi-Faced Independence: A Representation-Theoretic Approach. Journal of Functional Analysis 285, no. 3, 109907, doi:10.1016/j.jfa.2023.109907.

All publications

Preprint articles

Gerhold, M.: Schoenberg correspondence for multifaced independence. Preprint, arxiv.org/abs/2104.02985.

Published or accepted articles

Baraquin, I.; Franz, U.; Gerhold, M.; Kula, A.; Tobolski, M.: Free resolutions for free unitary quantum groups and universal cosovereign Hopf algebras. Journal of the London Mathematical Society 109(4), e12898, doi:10.1112/jlms.12898.
Gerhold, M.; Varšo, P.: Towards a classification of multi-faced independences: a combinatorial approach. Preprint, arXiv:2301.01816. To appear in Algebraic Combinatorics.
Gerhold, M.: Bimonotone Brownian Motion. In: N. Watanabe, L. Accardi, and S. Si (editors), Infinite Dimension Analysis, Quantum Probability and Related Topics, proceedings of QP38, special issue dedicated to Prof. Accardi, Prof. Volovich and a memorial issue to Prof. Hida, volume 32 of QP–PQ: Quantum Probab. White Noise Anal. World Sci. Publ., Hackensack, NJ, 2023. doi:10.1142/9789811275999_0005, 14 pp., preprint (2017) available at arxiv.org/abs/1708.03510.
Gerhold, M.; Shalit, O.: Bounded perturbations of the Heisenberg commutation relation via dilation theory. Proceedings of the AMS 151(9), 3949–3957, doi:10.1090/proc/16456.
Gerhold, M.; Hasebe, T.; Ulrich, M.: Towards a Classification of Multi-Faced Independence: A Representation-Theoretic Approach. Journal of Functional Analysis 285, no. 3, 109907, doi:10.1016/j.jfa.2023.109907.
Diehl, J.; Gerhold, M.; Gilliers, N.: Shuffle Algebras and Non-Commutative Probability for Pairs of Faces. SIGMA Symmetry Integrability Geom. Methods Appl. 19 (2023), Paper No. 006, 50 pp., doi:10.3842/SIGMA.2023.006.
Gerhold M.; Lachs, S.; Schürmann, M.: Categorial independence and Lévy processes. SIGMA Symmetry Integrability Geom. Methods Appl. 18 (2022), Paper No. 075, 27 pp., doi:10.3842/SIGMA.2022.075.
Gerhold M.; Pandey, S.; Shalit, O.; Solel, B.: Dilations of unitary tuples. J. Lond. Math. Soc. (2) 104 (2021), no. 5, 2053 – 2081, doi:10.1112/jlms.12491.
Gerhold M.; Shalit, O.: On the matrix range of random matrices. J. Operator Theory 85 (2021), no. 2, 527 – 545, jot.theta.ro/jot/archive/2021-085-002/2021-085-002-011.html.
Gerhold M.; Shalit, O.: Dilations of q-Commuting Unitaries. Int. Math. Res. Not. 2022, no. 1, 63 – 88, doi:10.1093/imrn/rnaa093.
Gerhold, M.; Skeide, M.: Interacting Fock Spaces and Subproduct Systems. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 23, no. 3, 2050017, 53 pp., doi:10.1142/S0219025720500174.
Gerhold, M.; Skeide, M.: Subproduct Systems and Cartesian Systems: New Results on Factorial Languages and their Relations with Other Areas. J. Stoch. Anal. 1, no. 4, Art. 5, 21 pp., doi:10.31390/josa.1.4.05.
Bichon, J.; Franz, U.; Gerhold, M.: Homological properties of quantum permutation algebras. New York J. Math. 23 (2017) 1671-1695, nyjm.albany.edu/j/2017/23-74.html.
Franz U.; Gerhold M.; Thom A.: On the Lévy-Khinchin Decomposition of Generating Functionals. Commun. Stoch. Anal. 9 (2015), no. 4, 529 – 544, doi:10.31390/cosa.9.4.06.
Gerhold, M.; Lachs, S.: Classification and GNS-construction for general universal products. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 18 (2015), no. 1, doi:10.1142/S0219025715500046.
Gerhold, M.; Kietzmann, S.; Lachs, S.: Additive deformations of braided Hopf algebras. Noncommutative harmonic analysis with applications to probability III, 175 – 191, Banach Center Publ., 96, Polish Acad. Sci. Inst. Math., Warsaw, 2012, doi:10.4064/bc96-0-11.
Gerhold, M.: Additive deformations of Hopf algebras. J. Algebra 339 (2011), 114 – 134, doi:10.1016/j.jalgebra.2011.05.019.

Theses

On several problems in the theory of comonoidal systems and subproduct systems
(Dissertation, Greifswald, supervisor: Michael Schürmann)
urn:nbn:de:gbv:9-002244-6
Quanten-Lévy-Prozesse auf Deformationen von Bialgebren
(Diploma Thesis, Greifswald, supervisor: Michael Schürmann)
pdf from math-inf.uni-greifswald.de

Extended abstracts

Classification of two-faced independences. RIMS Kôkyûroku No. ?: Mathematical aspects of quantum fields and related topics (submitted)
Applications of free probability to dilation theory (extended abstract). Oberwolfach Workshop 2010: Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability. Report No. 12/2020, 661 – 662, doi:10.14760/OWR-2020-12.
Bimonotone quantum Lévy processes (extended abstract). Oberwolfach Workshop 1819: Interactions between Operator Space Theory and Quantum Probability with Applications to Quantum Information. Report No. 22/2018, 1354 – 1355, doi:10.14760/OWR-2018-22.